Delete objects of incomplete type

This one made me think:

class X;

void foo(X* p)
{
    delete p;
}

How can we possibly delete p if we do not even know whether X has visible destructor? g++ 4.5.1 gives three warnings:

warning: possible problem detected in invocation of delete operator:
warning: 'p' has incomplete type
warning: forward declaration of 'struct X'

And then it says:

note: neither the destructor nor the class-specific operator delete will be called, even if they are declared when the class is defined.

Wow... are compilers required to diagnose this situation like g++ does? Or is it undefined behavior?